Chapter 3 - Derivatives - 3.9 Derivatives of Logarithmic and Exponential Functions - 3.9 Exercises - Page 211: 36

\[{f^,}\,\left( x \right) = 2\sqrt 2 {x^{\sqrt 2 - 1}}\]

\[\begin{gathered} f\,\left( x \right) = 2{x^{\sqrt 2 }} \hfill \\ \hfill \\ using\,\,the\,\,power\,\,rule \hfill \\ \hfill \\ {f^,}\,\left( x \right) = n{x^{n - 1}} \hfill \\ \hfill \\ then \hfill \\ \hfill \\ {f^,}\,\left( x \right) = 2\sqrt 2 {x^{\sqrt 2 - 1}} \hfill \\ \hfill \\ \end{gathered} \]